The most common names for these were film disc cutouts or "dimes" (because they were about the size and shape of a dime.) I don't have any more or I'd post a photo of one. They were a kind of shunt, passing extremely low current across them until the bulb they were shunting failed. Then the high voltage in the series circuit would arc through them fusing the sides together and completing a relatively resistance free circuit.

To understand how these cutouts fit into the design of series lamps, here's a feature on an old Line Material series street light that shows the components.

BTW, what they mean by open loop and closed loop is that in an open loop only one conductor is on each pole and the circuit makes a big open loop around town. A closed loop has both conductors on each utility pole.

I've seen photos of the socket with the prongs on the top that the cutout fits into (there's even one on eBay). My question is what holds the socket in the light? I couldn't see any method of holding the socket into the head or making electrical the connection to it.

There are side contacts, that fit to the disc area, so when the socket is removed, thes contact short out, so keep the rest of the string working.

These jaw-like contacts press into the indentions on the socket blades to hold the socket in the luminare from falling out, and as just explained they have enough tension to close together any time the socket is removed.

Here are some better pix of a series socket with a film cutout rupture disc. This disk had melted through so it's not as clean looking as a new one but you can get an idea as to its size and how close the tolerances are between the socket blades.

Here's a site for a company that still sells film cutouts. It shows all four breakover voltages. Before you run out and buy some, please note that a bottle of 100 discs is up to $370.00! Between the high cost of series incandescent bulbs and discs, not counting the higher electricity costs, the last remaining series incandescent systems may disappear sooner rather than later.

Here's the original 1900 patent drawing for the Jones socket that became the industry standard. The final patent wasn't awarded for nearly 6 years because of a challenge regarding the Thomson light bulb that had built in film cutouts. Jones' improvement was that the string didn't go dark when the bulb was being changed. Plus for radial waves and admiral's hats it was easier to change the bulbs from the ground using a lamp changing pole.